Different rock cutting tools were simulated, namely a chisel-shaped tool and a button-shaped tool. The numerical cutting tools were treated as rigid walls to simplify the simulation and the tool forces were therefore not influenced by wearing of the cutting tool. In each simulation the cutting tools advanced at a constant velocity. The tool forces, in three orthogonal directions, were recorded during the numerical simulations and the peak cutting forces were also predicted by theoretical equations. The damage to the assemblies, representing Paarl granite and Sandstone-2, was revealed as broken bonds, which merge into macroscopic fractures. The mean peak cutting forces obtained from numerical, theoretical and experimental models (from the literature) were compared. It was pointed out that the influence of cutting depth and wear plays a substantial part in the cutting process and has to be included in the numerical simulation for the results to be accurate and verifiable.